A theory of minimal realizations of rational matrix functions $W(\lambda)$
in the ``pencil'' form $W(\lambda)=C(\lambda A_1-A_2)^{-1}B$ is developed.
In particular, properties of the pencil $\lambda A_1-A_2$ are discussed when
$W(\lambda)$ is hermitian on the real line, and when $W(\lambda)$ is
hermitian on the unit circle.